Heat the oven to 400°. Snap the
tough ends off the asparagus and discard them. Cut the spears into 1-inch
pieces. Put the asparagus on a baking sheet and toss with the oil and 1/4
teaspoon each of the salt and pepper. Roast until tender, about 10 minutes.

Meanwhile, put the vinegar in a
small saucepan. Simmer until 3 tablespoons remain. Stir in the brown sugar and
the remaining 1/4 teaspoon pepper. Remove from the heat.

Cook the pasta in a large pot of
boiling, salted water until just done, about 13 minutes. Drain the pasta and
toss with the butter, vinegar, asparagus, Parmesan, and the remaining 1 3/4
teaspoons salt. Serve with additional Parmesan.